For the first time, a one-dimensional cellular automaton is proven ergodic under both very low and very high uniform noise while being non-ergodic at an intermediate noise rate.
Probabilistic cellular automata with Andrei Toom
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A perturbed cellular automaton with two phase transitions for the ergodicity
For the first time, a one-dimensional cellular automaton is proven ergodic under both very low and very high uniform noise while being non-ergodic at an intermediate noise rate.